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# If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values

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Re: If y = |2 + x| - |2 x| and |2x 15| < 2, how many integer values [#permalink]
I went with this approach as well:

First find the range of values for x:

Inequalities involving absolute values - here you have a number case again. First solve like this without the brackets:

2x – 15 < 2
2x < 17
x < 8.5

Second case (FLIP the sign and put a negative sign around the other side of the inequality):

2x – 15 > -2
x>6.5

Hence: 6.5<x<8.5 >>> however here I went a step further:
y = 2+x−(−(2−x))
y = 4 + 2x
6.5 < 2x + 4 < 8.5
2.5 < 2x < 4.5
2.5/2 < x < 4.5/2
the only integer value in this range is 2 so that's the only answer, is this logic sound?
Re: If y = |2 + x| - |2 x| and |2x 15| < 2, how many integer values [#permalink]
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